TILA-S: Timing-Driven Incremental Layer Assignment Avoiding Slew Violations

As very large scale integration technology scales to deep submicrometer and beyond, interconnect delay greatly limits the circuit performance. The traditional 2-D global routing and subsequent net by net assignment of available empty tracks on various layers lacks a global view for timing optimization. To overcome the limitation, this paper presents a timing driven incremental layer assignment tool, to reassign layers among routing segments of critical nets and noncritical nets. Lagrangian relaxation techniques are proposed to iteratively provide consistent layer/via assignments. Modeling via min-cost flow for layer shuffling avoids using integer programming and yet guarantees integer solutions via uni-modular property of the inherent model. In addition, multiprocessing of K × K partitions of the whole chip provides runtime speed up. Furthermore, a slew targeted optimization is presented to reduce the number of violations incrementally through iteration-based Lagrangian relaxation, followed by a post greedy algorithm to fix local violations. Certain parameters introduced in the models provide tradeoff between timing optimization and via count. Experimental results in both ISPD 2008 and industry benchmark suites demonstrate the effectiveness of the proposed incremental algorithms.